Systems of colliding bodies in a gravitational field: Evolution and role of the internal rotations

To emphasize the rotational effects of a simple friction between colliding bodies in a keplerian field we investigate numerically the evolution of the rotational energies in a three dimensional system of spherical particles interacting through inelastic collisions in a deterministic model. All the particles are made of the same material but they possibly have different sizes. Each collision reduces the relative surface velocity and there are exchanges between orbital energy and rotational energy. Our results are compared with some previous papers and our aim is to supply other probabilists models with simple basic references about mean dynamical properties.The rotational energy of the colliding bodies tends to reach an equilibrium state that depends only on the rate of energy loss in the collision process. Internal rotations prevent the complete flattening of the system. With this model, light and small particles spin faster than the massive and big ones. We observe an excess of prograde rotations on counterclockwise orbits. The ratio of rotational and orbital energies is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa% aaleaacaWGYbaabeaakiaac+cacaWGfbWaaSbaaSqaaiaadUgaaeqa% aOGaeyisISRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaa% aaaa!3F83!\[E_r /E_k \approx 10^{ - 3} \] while the ratio of corresponding mean angular velocities is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaacq% aHjpWDaiaawMYicaGLQmcacaGGVaWaaaWaaeaacqGHPoWvaiaawMYi% caGLQmcacqGHijYUcaaIYaaaaa!4008!\[\left\langle \omega \right\rangle /\left\langle \Omega \right\rangle \approx 2\] These values depends strongly on the dimensional scale of the model.     

Fast Segmentation of Solar Extreme Ultraviolet Images

A segmentation scheme for identifying large-scale structures (coronal holes, active regions, etc.) in solar extreme ultraviolet images, is presented. Unlike standard approaches, both the image intensity and the relative contribution of different wavelengths are used. Spectral information is important for compensating luminosity changes. The approach is illustrated with images taken in the extreme ultraviolet by the EIT telescope onboard SOHO. This supervised segmentation scheme, which incorporates a Bayesian classifier, is computationally simple, and can easily be used to track in near-real time structures, such as coronal holes.     

The dynamical structure of dwarf elliptical galaxies

Deep imaging and long-slit spectroscopy was obtained for a sample of dwarf ellipticals in the Fornax cluster, NGC 5044 and NGC 5898 groups using the ESO VLT. The observational data extend out to typically 1.5–2 effective radii and indicate a kinematic dichotomy in the family of ellipticals. The observed stellar kinematics indicate a luminosity–velocity dispersion relation largely supporting Supernova-driven stellar mass loss scenarios for the formation of dwarf ellipticals. Stellar dynamical models favour dark matter halos with typical mass-to-light ratios in the range of 3 to 9 solar units. This revised version was published online in August 2006 with corrections to the Cover Date.     

Beam Mode Expansion of Corrugated Conical Horns with Phase Correcting Lens: Application to Radioastronomy Receivers

A classical radioastronomy receiver is fed with a corrugated horn and an independent lens, both placed in a cryostat to lower the noise temperature. The beam is focused and directed using a combination of elliptical and plane mirrors. This paper proposes modifying the initial feeding system by placing the lens onto the horn aperture, thereby allowing a size reduction of the horn and lens, and a simplification of their mechanical design. The profiled lens is shaped to correct the phase error on the horn aperture. A quasi-optical model of the horn-plus-lens system has been developed using a Beam Mode Expansion (BME). Results using both a hyperbolic-planar lens and a spherical-elliptical lens, as well as results obtained by using Geometrical Optics (GO) with a Kirchoff–Huygens integration to get the far-field pattern, have been compared with measurements. As a direct application, a full focusing system for the new 40-m radiotelescope at the “Centro Astronómico de Yebes” is presented for the 22, 30 and 45 GHz bands. This paper has developed a QO model for a corrugated conical horn with a phase-correcting lens. This revised version was published online in July 2006 with corrections to the Cover Date.     

The evolutionary history of early-type galaxies as derived from the fundamental plane

The fundamental plane (FP) scaling relations and their evolution are a powerful tool for studying the global properties of early-type galaxies and their evolutionary history. The form of the FP, as derived by surveys in the local Universe at wavelengths ranging from the U to the K band, cannot be explained by metallicity variations alone among early-type galaxies; systematic variations in age, dark matter content, or homology breaking are required. A large-scale study of early-type galaxies at 0.1 < z < 0.6demonstrates that the SB intercept of the FP, the rest frame (U-V) colour, and the absorption line strengths all evolve passively, thereby implying a high mean formation redshift for the stellar content. The slope of the FP evolves with redshift, which is broadly consistent with systematic age effects occurring along the early-type galaxy sequence. The implication that the least luminous early-type galaxies formed later than the luminous galaxies is discussed in the context of the evolution of thecolour–magnitude relation, the Butcher–Oemler effect and hierarchical galaxy formation models. This revised version was published online in July 2006 with corrections to the Cover Date.     

Envelopes of rapidly rotating neutron stars

Motivated by the discovery of the millisecond pulsars, we consider the effect of rapid rotation on the envelope of a neutron star. Solving the equation of hydrostatic equilibrium we find expressions for the density and oblateness as functions of radius and polar angle.     

Poisson-distributed patterns of explosive eruptive activity

The study of patterns of eruption occurrence could lead to a better understanding of the physics behind the volcanic process. However, various attempts to find a single statistical distribution that describes the occurrences of volcanic eruptions have not been successful. Global data show that, if the energies of point events in time (eruptions) are properly accounted above a certain noise level, the stochastic process — whose realization consists of explosive volcanic events — can be well represened by a Poisson point process, though not necessarily stationary. Many previous attempts to describe patterns of eruption occurrences were hampered by counting events with all levels of explosivity in the same category. When eruptions are separated by their sizes, the occurrence patterns of the higher magnitude eruptions become clearly Poissonian. In this study eruptions are classified by size using the Volcanic Explosivity Index (Newhall and Self 1982). Further analysis of the magnitude-characterized eruption data shows direct relations among the energy of eruptions, mean rate of occurrences and distribution of repose intervals between eruptions. An important result from the analysis of energy and mean rate of occurrence data is that, for global data, the product of those parameters is a constant. Simple load-and-discharge models provide an explanation of the random features of the volcanic processes. These considerations lead to the definition of a constinuous magnitude scale for volcanic eruptions which can consistently measure the energy and the rate-of-occurrence of eruptions over a wide range of values.     

Crustal and upper mantle structures of the brazilian coast

The Rayleigh wave phase and group velocities in the period range of 24–39 sec, obtained from two earthquakes which occurred in northeastern brazil and which were recorded by the Brazilian seismological station RDJ (Rio de Janeiro), have been used to study crustal and upper mantle structures of the Brazilian coastal region. Three crustal and upper mantle models have been tried out to explain crustal and upper mantle structures of the region. The upper crust has not been resolved, due basically to the narrow period range of the phase and group velocities data. The phase velocity inversions have exhibited good resolutions for both lower crust and upper mantle, with shear wave velocities characteristic of these regions. The group velocity data inversions for these models have showed good results only for the lower crust. The shear wave velocities of the lower crust (3.86 and 3.89 km/sec), obtained with phase velocity inversions, are similar to that (=3.89 km/sec) found byHwang (1985) to the eastern South American region, while group velocity inversions have presented shear velocity (=3.75 km/sec) similar to that (=3.78 km/sec) found byLazcano (1972) to the Brazilian shield. It was not possible to define sharply the crust-mantle transition, but an analysis of the phase and group velocity inversions results has indicated that the total thickness of the crust should be between 30 and 39 km. The crustal and upper mantle model, obtained with phase velocity inversion, can be used as a preliminary model for the Brazilian coast.     

Evaluation of ferrous and ferric Mössbauer fractions

The Mössbauer fractions f for various ferrous- and/or ferric-containing oxides and oxyhydroxides, silicates and carbonates were evaluated from the experimental temperature dependence of their center shifts, using the Debye approximation for the second-order Doppler shift. It is concluded that ferrous ions exhibit a lower fraction as compared to ferric ions. Using standard mixtures of -Fe₂O₃ with selected Fe²⁺ or Fe³⁺ compounds, it is found that the calculated Fe³⁺ f values are somewhat overestimated with respect to those of Fe²⁺. Possible explanations for this shortcoming are discussed and it is suggested that a different temperature dependence of the intrinsic isomer shift is the most likely reason. This suggestion is corroborated by analyses of hematite and hedenbergite data which are available for temperatures up to 900 K and 800 K respectively.